Optimal Investment with a Noisy Signal of Future Stock Prices

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-01-21 DOI:10.1007/s00245-023-10099-x

Peter Bank, Yan Dolinsky

引用次数: 0

Abstract

We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock’s price fluctuations. With linear temporary price impact the resulting optimal investment problem with exponential utility turns out to be not only well posed, but it even allows for a closed-form solution. We describe this solution and the resulting problem value for this stochastic control problem with partial observation by solving its convex-analytic dual problem.

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利用未来股票价格的噪声信号进行最优投资

我们考虑的是一个投资者，他对驱动股票价格波动的独立布朗运动之一的未来演变有动态的了解。在线性临时价格影响的情况下，所产生的指数效用最优投资问题不仅可以很好地求解，甚至可以得到闭式解。我们通过求解其凸解析对偶问题，描述了这个具有部分观测的随机控制问题的解和问题值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.